Final answer:
The equation provided is a differential equation, but it is not clear how to solve it as it is presented because it is not separable, exact, nor is an integrating factor provided. Additional context or a different method may be necessary to find a solution.
Step-by-step explanation:
The student has presented a differential equation: 2(x² + y²)dx + 9xydy = 0. To solve this equation, we need to find a way to separate the variables x and y. However, based on the provided information, it does not appear to be separable or exact, and no integrating factor is immediately evident. It is possible that additional context or constraints are needed to solve it, such as a given relationship between x and y, or it might require a numerical or graphical approach.